Police have a connection from a member of R. Kelly's entourage to a shooting threat made during a screening of the "Surviving R. Kelly" docuseries ... TMZ has learned.

Law enforcement sources tell us ... NYPD has Donnel Russell listed as a person of interest for the incident that went down last month in NYC. We know Russell is a business associate of Kelly. We're told police want to speak to him about the threats that were phoned into a theater as it was showing the Lifetime docuseries.

As we reported ... someone called the NeueHouse just 20 minutes into the screening, and warned someone in the audience would start shooting up the place if the program continued. The venue was immediately evacuated.

Cops tracked the number down to a man with a Chicago-based 773 area code. We're told police have connected that number to Russell, and have attempted to make contact with him, but have had no luck thus far in reaching him directly.

Interestingly enough, the father of Joycelyn Savage, one of Kelly's alleged sex slaves, filed a police report last week in Georgia claiming a guy by the name of Don Russell texted him threats right before 'Surviving' aired on TV.

Our law enforcement sources tell us they believe that "Don" is the same Donnel Russell the NYPD is trying to contact.